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The purpose of this paper is to study thermal (natural) convection in nine different containers involving the same area (area= 1 sq. unit) and identical heat input at the bottom wall (isothermal/sinusoidal heating). Containers are categorized into three classes based on geometric configurations [Class 1 (square, tilted square and parallelogram), Class 2 (trapezoidal type 1, trapezoidal type 2 and triangle) and Class 3 (convex, concave and triangle with curved hypotenuse)].

The governing equations are solved by using the Galerkin finite element method for various processing fluids (Pr = 0.025 and 155) and Rayleigh numbers (10³ ≤ Ra ≤ 10⁵) involving nine different containers. Finite element-based heat flow visualization via heatlines has been adopted to study heat distribution at various sections. Average Nusselt number at the bottom wall ( Nub¯) and spatially average temperature (θ^) have also been calculated based on finite element basis functions.

Based on enhanced heating criteria (higher Nub¯ and higher θ^), the containers are preferred as follows, Class 1: square and parallelogram, Class 2: trapezoidal type 1 and trapezoidal type 2 and Class 3: convex (higher θ^) and concave (higher Nub¯).

The comparison of heat flow distributions and isotherms in nine containers gives a clear perspective for choosing appropriate containers at various process parameters (Pr and Ra). The results for current work may be useful to obtain enhancement of the thermal processing rate in various process industries.

Heatlines provide a complete understanding of heat flow path and heat distribution within nine containers. Various cold zones and thermal mixing zones have been highlighted and these zones are found to be altered with various shapes of containers. The importance of containers with curved walls for enhanced thermal processing rate is clearly established.

This paper aims to study the effect of concentric hot circular cylinder inside egg-cavity porous-copper nanofluid on natural convection phenomena.

The finite element method–based Galerkin approach is applied to solve numerically the set of governing equations with appropriate boundary conditions.

The effects of different range parameters, such as Darcy number (10–3 = Da = 10–1), Rayleigh number (103 = Ra = 106), nanoparticle volume fraction (0 = ϑ = 0.06) and eccentricity (−0.3 = e = 0.1) on the fluid flow represent by stream function and heat transfer represent by temperature distribution, local and average Nusselt numbers.

A comparison between oval shape and concentric circular concentric cylinder was investigated.

In the current numerical study, heat transfer by natural convection was identified inside the new design of egg-shaped cavity as a result of the presence of a circular inside it supported by a porous medium filled with a nanofluid. After reviewing previous studies and considering the importance of heat transfer by free convection inside tubes for many applications, to the best of the authors’ knowledge, the current work is the first study that deals with a study and comparison between the common shape (concentric circular tubes) and the new shape (egg-shaped cavity).

This paper aims to conduct numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the incompressible smoothed particle hydrodynamics (ISPH) method.

In the ISPH method, the pressure evaluation is stabilized by including both of divergence of velocity and density invariance in solving pressure Poisson equation. The authors prevented the particles anisotropic distributions by using the shifting technique.

The proposed ISPH method exhibited good performance in natural/mixed convection in a cavity with fixed, moving and free-falling rigid body. In natural convection, the authors investigated the effects of an inner sloshing baffle as well as fixed and moving circular cylinders on the heat transfer and fluid flow. The heated baffle has higher effects on the heat transfer rate compared to a cooled baffle. In the mixed convection, a free-falling circular cylinder over a free surface cavity and heat transfer in the presence of a circular cylinder in a lid-driven cavity are simulated. Fixed or moving rigid body in a cavity results in considerable effects on the heat transfer rate and fluid flow.

The authors conducted numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the ISPH method.

This study aims to show the importance of natural convection of supercritical fluid in an inclined cavity. The heat transfer performance of natural convection can be improved.

A model of an inclined cavity was set up to simulate the natural convection of supercritical fluid. The influence of inclined angles (30 to approximately 90°) and pressures (8 to approximately 12 MPa) are analyzed. To ascertain flow and heat transfer of supercritical fluid natural convection, this paper conducts a numerical investigation using the lattice Boltzmann method (LBM), which is proven to be precise and convenient.

The results show that the higher heat transfer performance can be obtained with an inclined angle of 30°. It is also presented that the heat transfer performance under pressure of 10 MPa is the best. In addition, common criterion number correlations of average Nusselt number are also fitted.

These study results can provide a theoretical reference for the study of heat transfer of supercritical fluid natural convection in engineering.

The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed.

This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities.

Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers.

This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.

External natural convection is rarely studied by numerical simulation in the literature due to the fact that flow of interest takes place in an unbounded domain and that if a limited computational domain is used the corresponding outer boundary conditions are unknown. In this study, we propose outer boundary conditions for a limited computational domain and make the corresponding numerical implementation in the scope of a projection method combining spectral methods and domain decomposition techniques. Numerical simulations are performed for both steady natural convection about an isothermal cylinder and transient natural convection around a line‐source. An experiment is also realized in water using particle image velocimetry and thermocouples to make a comparison during transients of external natural convection around a platinum wire heated by Joule effect. Good agreement, observed between numerical simulations and experiments, validated the outer boundary conditions proposed and their numerical implementation. It is also shown that, if one tolerates prediction error, numerical results obtained remain at least reasonable in a region near the line‐source during the entire transients. We thus paved the way for numerical simulation of external natural convection although further studies remain to be done for higher heating power (higher Rayleigh number).

Two‐dimensional finite difference calculations are carried out to study laminar flow in longitudinal and transverse convection rolls for three different geometries: a single rectangular cavity with high aspect ratio; a double cavity with a thin separation sheet; and a double cavity with a separation sheet and a honeycomb structure. The equations for the convection‐diffusion in the fluid and conduction in the solid region are solved simultaneously. Good agreement with experimental data is achieved for Rayleigh numbers not too high above the critical value for the onset of secondary convection rolls (Ra < 8500 for vertical and Ra < 2700 for horizontal cavities filled with air). Simulation fails for inclined cavities, where the flow structure is essentially three‐dimensional.

The purpose of this paper is to investigate the effects of gravitational modulation on natural convection in a square inclined porous cavity filled by a fluid containing copper nanoparticles.

The present study uses a system of equations that couple hydrodynamics to heat transfer, representing the governing equations of fluid flow in a square domain. The Boussinesq–Darcy flow with Cu-water nanofluid is considered. The dimensionless partial differential equations are solved numerically using finite difference method based on alternating direction implicit scheme. The cavity is differentially heated by constant heat flux, while the top and bottom walls are insulated. The authors examined the effects of gravity amplitude (λ), vibration frequency (σ), tilt angle (α) and Rayleigh number (Ra) on flow and temperature.

The numerical simulations, in the form of streamlines, isotherms, Nusselt number and maximum stream function for different values of amplitude, frequency, tilt angle and Rayleigh number, have revealed an oscillatory behavior in the development of flow and temperature under gravity modulation. An increase of amplitude from 0.5 to 1 intensifies the flow stream (from |ψ_max| = 21.415 to |ψ_max| = 25.262) and improves heat transfer (from Nu¯ = 17.592 to Nu¯ = 20.421). Low-frequency vibration below 50 has a significant impact on the flow and thermal distributions. However, once this threshold is exceeded, the flow weakens, leading to a gradual decrease in heat transfer rate. The inclination angle is an effective parameter for controlling the flow and temperature characteristics. Thus, transitioning the tilt angle from 30° to 60° can increase the flow velocity (from 22.283 to 23.288) while reducing the Nusselt number (from 16.603 to 13.874). Therefore, by manipulating the combination of vibration and inclination, it is founded that for a fixed frequency value of σ = 100 and for increased amplitude (from 0.5 to 1), the flow intensity at inclination of 60° is boosted, and an increase of the heat transfer rate at inclination of 30° is also observed. Convective thermal instabilities may arise depending on the different key factors.

To the best of the authors’ knowledge, this study is original in its examination of the combined effects of modulated gravity and cavity inclination on free convection in nanofluid porous media. It highlights the crucial roles of these two important factors in influencing flow and heat transfer properties.

The purpose of this paper is to investigate the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.

Analytical solution in terms of Bessel’s function and modified Bessel’s function of order 0 and 1 is obtained for velocity, temperature, Nusselt number, skin friction and mass flow rate.

It is established that the role of Knudsen number and fluid–wall interaction parameter is to decrease fluid temperature, velocity, Nusselt number and skin friction.

No laboratory practical or experiment was conducted.

Cooling device in electronic panels, card and micro-chips is frequently cooled by natural convection.

In view of the amount of works done on natural convection in microchannel, it becomes interesting to investigate the effect that time-periodic heating has on natural convection flow in a vertical micro-annulus. The purpose of this paper is to examine the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.

The purpose of this paper is to evaluate the capacity of two equation turbulence models to reproduce mean and fluctuating quantities in the case of both natural convection and isothermal flows.

Numerical predictions of mean velocity profiles, air and wall temperatures as well as turbulent kinetic energy by three different two equation models (standard k‐ε, renormalisation group k‐ε and shear‐stress transport‐k‐ω) are compared with corresponding experimental values.

The prediction of mean velocities and temperatures is in all cases satisfactory. On the other hand, the prediction of turbulent quantities is less precise.

The three models under consideration in this paper can be used for engineering applications such as HVAC calculations.